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What is the value of 36x^2 - 108xy + 81y^2?

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Joined: 02 Sep 2009
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What is the value of 36x^2 - 108xy + 81y^2?  [#permalink]

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New post 10 Aug 2018, 02:50
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (01:36) correct 31% (02:46) wrong based on 61 sessions

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What is the value of 36x^2 - 108xy + 81y^2?  [#permalink]

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New post Updated on: 10 Aug 2018, 04:03
We need (6x-9y)^2 = 9(2x - 3y)^2

S1: Sufficient

S2: x = 5/y
x = 1, y = 5 --> 2x - 3y = -13
y = 1, x = 5 --> 2x - 3y = 7
Clearly, not sufficient.

Answer: A

Originally posted by sandman13 on 10 Aug 2018, 03:14.
Last edited by sandman13 on 10 Aug 2018, 04:03, edited 1 time in total.
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Re: What is the value of 36x^2 - 108xy + 81y^2?  [#permalink]

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New post 10 Aug 2018, 04:00
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1
Bunuel wrote:
What is the value of \(36x^2 - 108xy + 81y^2\)?


(1) \(3y−2x=−4\)

(2) \(x=\frac{5}{y}\)


\(36x^2 - 108xy + 81y^2\)=\(9(4x^2 - 12xy + 9y^2)\)=\(9(3y-2x)^2\)

Re-phrased question stem:- \(9(3y-2x)^2\)=?

St1:- \(3y−2x=−4\)
Sufficient.(substitute the value of 3y-2x in rephrased question stem)

St2:- \(x=\frac{5}{y}\)
Insufficient. (Either value x or y is required)

Ans. (A)
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What is the value of 36x^2 - 108xy + 81y^2?  [#permalink]

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New post 13 Aug 2018, 06:45

Solution


Given:
    • An expression, \(36x^2 – 108xy + 81y^2\)

To find:
    • The value of the given expression, \(36x^2 – 108xy + 81y^2\)

Analysing Statement 1
“3y – 2x = -4”
    • Squaring on both sides, we get,
      o \(4x^2 – 12xy + 9y^2 = 16\)
    • Multiplying this equation by 9, we get
      o \(36x^2 – 108xy + 81y^2 = 144\)

Therefore, Statement (1) ALONE is sufficient to answer this question

Analysing Statement 2
“x = 5/y”
    • Substituting this in the required expression, we get,
      o \(180/y^2 – 540 + 81y^2\)
      o We cannot find the value of this expression as we do not have any further information about y.

Therefore, Statement (2) ALONE is not sufficient to answer this question

Hence, the correct answer is option A.

Answer: A

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